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Demand Estimation

Demand Estimation. Specifying a Demand Equation General Form: Q = F(P, M, P R ,T, P e , N) Empirical (Regression) Form: Q = a + bP + cM + dP R + eN You estimated a demand equation like this in the demand project. The Identification Problem. Estimate Q = a + bP + cM + dP R + eN

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Demand Estimation

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  1. Demand Estimation • Specifying a Demand Equation • General Form: • Q = F(P, M, PR,T, Pe, N) • Empirical (Regression) Form: • Q = a + bP + cM + dPR + eN • You estimated a demand equation like this in the demand project

  2. The Identification Problem • Estimate Q = a + bP + cM + dPR + eN • If P and Q are determined by supply and demand, how do you know that you are estimating a demand relationship? • Answer: You don’t! • If you have not estimated a demand relationship, you have an identification problem. • Warning signs: • Coefficient on price (b) is positive • Coefficient on price (b) is not statistically significant

  3. Solution to Identification Problem • Use a technique called 2-stage Least Squares • Specify Demand and Supply Equations • Qd = a + bP + cM + dPR + eN • Qs = f + gP +hPI • Run a 2-stage least squares program • When is Identification not a problem? • Data are for a single firm setting it’s own price • Price not set by market (regulated prices) • Electricity prices are regulated by the states • Identification not a problem for demand project

  4. Calculating Elasticities for estimated demand equations • Linear equation – demand project • Q = a + bP + cM + dPR + eN • E = b(P/Q) = (ΔQ/ΔP)(P/Q) • EM = c(M/Q); EPR = d(PR/Q) • Log-linear equation – constant elasticity • Ln(Q) = g + h(lnP) + j(lnM) + k(lnPR) • Coefficients (h, j, k) are elasticities • No calculation needed

  5. Calculate elasticities at the sample means • Milkwh= 10800 – 3581(Pkwh) + 0.004(Pop) + 2252(PGas) • Elasticity = (coeff.)(value/Milkwh) • Sample Means: Milkwh=25365 Pkwh=9.0 Pop=5,756,577 PGas=11.4 • E = -3581(9.0/25365) = -1.27 • Epop = 0.004(5,756,577/25365) = 0.91 • Epgas= 2252(11.4/25365) = 1.01

  6. Exercise: Elasticities • Milkwh= 10800 – 3581(Pkwh) + 0.004(Pop) + 2252(PGas) • Milkwh=38,526 Pkwh=6.92 Pgas=10.6 Pop=5,900,962 • Elasticity = (coeff.)(value/Milkwh) • Calculate electricity demand elasticities with respect to Pkwh, Pop, & Pgas • Ep = -0.643; Epop = 0.613; EPg = 0.62

  7. Forecasting Demand • Using Elasticities • Multiply elasticities by projected % changes in explanatory variables • Add the results to get projected % change in demand • Using linear regression equation • Multiply coefficients by projected values for explanatory variables in future period • Add results and intercept to get forecast of demand

  8. Forecasting with elasticities • Estimate a log-linear equation • LMilkwh = 0.04 – 0.92(LPkwh) + 1.0(LPop) + 0.4(LPgas) – 0.4(Linc) • Get projected % changes • Pkwh:10% Pop:1% Pgas:20% Inc:2% • Calculate the projected % change in Milkwh • -0.92(10%)+1.0(1%)+0.4(20%)-0.4(2%) = -1% • Do not use the intercept!It doesn’t change. • Suppose Pgas goes down by 20%, not up? • -0.92(10%)+1.0(1%)+0.4(-20%)-0.4(2%) = -17%

  9. Exercise: Forecasting with linear demand • Estimate a linear demand equation • Milkwh= 10800 – 3581(Pkwh) + 0.004(Pop) + 2252(PGas) • Get forecasts of explanatory variables • Pkwh=10 Pop=20,000,000 Pgas=10 • Calculate a Forecast for Milkwh • Milkwh=10800 – 3581(10) + 0.004(20,000,000) + 2252(10) • = 77,510 • Here the intercept is included in the calculation.

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